It is not given to everyone to have what it takes to fix and repair just about anything. But most of people are able to use their judgment and analytical skills to put them to good use. I will not write you a book on the topics as there are good article on Wikipedia about troubleshooting, but will try to draw a portrait of the skills required to be able to do the job fairly easily.
You need to be able to analyze a situation using a logical and cartesian approach. This refers to evaluating the functionalities in a step by step manner and think outside the box. To give you an idea of what I just meant, imagine having the nose at about 2 inches from a car engine block while trying to identify the squeaking noise on your right. It is hard for you to see what you should be looking for and in which context! Now, backup until you can see the whole engine compartment. You will then see that there is a belt turning to the right of the engine block and this is probably where the noise was coming from. Now by approaching your ear you will be able to narrow down to a specific place, where the noise is emerging from.
This is what I called, the step back - back in method. I use that a lot and it works. Always get the big picture and then zoom in toward the problematic area using all of you senses.
I know this is probably confusing for some people, but it is not obvious to put into words, the state of mind I am in when troubleshooting as there are lots a variables.
Please come back often as I may update this post to make it clearer!
Proceed to The steps... chapter